MOM 4UI Unit 5 - Day 8 More Combinations Questions 1, In how many ways can a committee of 5 be selected from 8 people? 2. A team consisting of 11 players is selected from a roster of 14 players a) How many arrangements of players are possible, b) There is only one goalkeeper in the roster who must be included on the team. How many arrangements are possible? 3, A three cord hand is dealt from a standard 52 deck of cords. a) How many different hands are possible? b) How many hands cordist of exactly three spades? 4. Five colours from a list of ten colours, Determine the number of combinations, if. a) there are no restrictions. b) red and green are always be included. c) red must be excluded, d) red and blue are always included, and purple is always excluded. 5. How many different triangles can be formed if each side is 5 am, 6 cm, 7 cm, 8 cm, or 9 cm long and all sides must have different lengths? 6. In how many ways can a committee of 6 persons be chosen from 5 men and 4 women if each committee is to consist of 3 men and 3 women? 7. A school council consists of 10 teachers and 12 students, In how many ways can a group of 6 be selected if the group consists of: 0) 3 teachers and 3 students b) 2 teachers and 4 students An organization has 20 members, four of whom are doctors, In how many ways can a committee of 4 be selected so as to include at least I doctor on each committee? 9, A group consists of 5 boys and B girls, In how many ways can a team of 5 be chosen if it is to contain: a) no girls? bj mo boys? c) at least 3 boys? 10. If a is a natural number, find a when11, If a is a natural number, find a when P(n,4)- 30 2 12. If 22 (22 find rif r+3 3-5 r+ 3 3r-5 Probability Questions 13, A four card hand is dealt from a standard 52 deck of cards. Determine the probability that hand contains a) Queen of Hearts, Ace of Spades, 7 of clubs, and 6 of hearts b) exactly 2 hearts cj at least 1 heart d) exactly 3 aces e) either pair of aces OR 2 face cards. (Carefull) 14. A committee of 5 students is to be chosen from 12 Kitchener residents and 7 Waterloo residents, Determine the probability that a) Addy, Maisie, Spencer, Braden, and Nicholas form the committee b) the committee has exactly 3 Waterloo residents c) the committee has at most 4 Kitchener residents, d) at least 2 residents from each city are on the committee, 2) the committee completely excludes residents from one of the two cities, Answers: 1, 56 20, 364 2b. 286 30. 22100 3b. 286 40, 252 4b. 56 4c. 126 4d, 35 5. 10 6, 40 70. 26400 76. 22275 8, 3025 90. 1 9b, 56 9c. 321 10, 17 11 8 12, 6 13a, 4446 188474 270725 13b, 20825 270725 13d. 192 1 385 270725 -13e. 57852 270725 140. 11626 : 14b. 389 14c. 1936 301 14d, 323 646 140. 271 3676